High Quality Content by WIKIPEDIA articles! In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both f:Mto N and its inverse f^{- 1}:Nto M are differentiable (if these functions are r times continuously differentiable, f is called a Cr-diffeomorphism).

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